Local Scott compactification
(English)Article in journal (Refereed) Submitted
We show how to embed certain formal topologies in locally Scott formal topologies. We call this process local Scott compactification. Examples include localic completions of metric spaces. We also prove a lifting result for morphisms. The local Scott compactification of a space corresponds to a domain representation of the space and in this way yields a space containing partial elements. In the case of the real numbers we obtain the space of partial reals, consisting of intervals where the endpoints are lower and upper reals respectively. We show that partial reals that define compact overt subspaces of the real numbers correspond precisely to intervals with real endpoints. The lifting of morphisms give sharp extensions of continuous real valued functions in the sense of interval analysis. These results are also generalized to normed vector spaces.
Formal topologies, Continuous dcpos, Locally compact metric spaces
Algebra and Logic
Research subject Mathematical Logic
IdentifiersURN: urn:nbn:se:uu:diva-152064OAI: oai:DiVA.org:uu-152064DiVA: diva2:412411